document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912101>Question 912101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the inverse of f(x) = 4-ln(x+2) ?\r<BR>\n" );
document.write( "\n" );
document.write( "what is the domain of the inverse function?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553571 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=553571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the inverse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+4-ln%28x%2B2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+4-ln%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=y ALIGN=MIDDLE  ALT=\"f%28x%29+=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4-ln%28x%2B2%29+ ALIGN=MIDDLE  ALT=\"y+=+4-ln%28x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...swap <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the inverse:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+4-ln%28y%2B2%29 ALIGN=MIDDLE  ALT=\"x=+4-ln%28y%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%2B2%29=+4-x ALIGN=MIDDLE  ALT=\"ln%28y%2B2%29=+4-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "by definition: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a+%2Cx+%29=+N ALIGN=MIDDLE  ALT=\"log%28a+%2Cx+%29=+N\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5EN=+x ALIGN=MIDDLE  ALT=\"a%5EN=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%2B2%29 ALIGN=MIDDLE  ALT=\"ln%28y%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,you have that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=e ALIGN=MIDDLE  ALT=\"a=e\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B2 ALIGN=MIDDLE  ALT=\"x=y%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=4-x ALIGN=MIDDLE  ALT=\"N=4-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%284-x%29=+y%2B2 ALIGN=MIDDLE  ALT=\"e%5E%284-x%29=+y%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=e%5E%284-x%29-2 ALIGN=MIDDLE  ALT=\"+y=e%5E%284-x%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29=y ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29+%28x%29+=e%5E%284-x%29-2 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29+%28x%29+=e%5E%284-x%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29+%28x%29+=+-e%5E%28-x%29+%282e%5Ex-e%5E4%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29+%28x%29+=+-e%5E%28-x%29+%282e%5Ex-e%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "domain: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (all real numbers)\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4-ln%28x%2B2%29%2C+e%5E%284-x%29-2%2Cx%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4-ln%28x%2B2%29%2C+e%5E%284-x%29-2%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );